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C5×C7×(C13⋊C3)⋊D7 #34062067

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(C5×C7×D7)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC7×C13 ⋊ C2×C3×C5×C7
HallC5×C72×C13⋊C3 ⋊ C2
HallC5×C7×D91 ⋊ C3
HallC72×C13⋊C3 ⋊ C2×C5
HallC7×D91 ⋊ C3×C5
HallC72×C13 ⋊ C2×C3×C5
HallC5×C72 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C7×D7
HallC5×C13 ⋊ C3×C7×D7
SylowC72 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ C5×C7×D7
SylowC13 ⋊ C3×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC5×C7(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D7×D13⋊C3, C5×D7×(C13⋊C3)⋊D7, C5×((C13⋊C3)⋊D7)⋊D7, …
maximal normal subgroup ofC5×C7×D7×D13⋊C3, C5×D7×(C13⋊C3)⋊D7, C5×((C13⋊C3)⋊D7)⋊D7, …
maximal quotient ofC5×C7×#11763955, C2×C5×C7×(C13⋊C3)⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 60);